In DC steady-state, what is the behavior of capacitors and inductors?

In DC steady-state, what is the behavior of capacitors and inductors?

• A. Capacitors open-circuit; inductors short-circuit.
• B. Capacitors short-circuit; inductors open-circuit.
• C. Both capacitors and inductors behave as short circuits.
• D. Both capacitors and inductors behave as open circuits.

Answer: (A)

In DC steady-state, a capacitor blocks constant voltage while an inductor allows constant current. This comes from their impedances: Z_C = 1/(jωC) and Z_L = jωL. When the signal is purely DC, ω is zero, so Z_C becomes infinite, meaning no DC current can flow through a capacitor—it's effectively open. At the same time, Z_L goes to zero, so an inductor provides a direct path for DC current—it's effectively a short. Real components have small resistances and leakage, but the ideal model uses open for capacitors and short for inductors in steady-state DC. This is why the correct behavior is a capacitor as an open circuit and an inductor as a short circuit.

In DC steady-state, a capacitor blocks constant voltage while an inductor allows constant current. This comes from their impedances: Z_C = 1/(jωC) and Z_L = jωL. When the signal is purely DC, ω is zero, so Z_C becomes infinite, meaning no DC current can flow through a capacitor—it's effectively open. At the same time, Z_L goes to zero, so an inductor provides a direct path for DC current—it's effectively a short. Real components have small resistances and leakage, but the ideal model uses open for capacitors and short for inductors in steady-state DC. This is why the correct behavior is a capacitor as an open circuit and an inductor as a short circuit.